CN117200873B - Calculation unloading method considering satellite mobility in satellite edge calculation network - Google Patents
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Abstract
The calculation unloading method considering satellite mobility in the satellite edge calculation network can unload the user task to the satellite for calculation, thereby rapidly responding to the user service request and reducing the resource and energy consumption; analyzing four scenes of satellite movement, establishing a time delay model considering the satellite movement, and establishing an optimization problem of calculation and unloading according to the time delay and energy consumption model, so that the problem of high satellite movement speed is effectively solved; and solving the problem by using an ADMM algorithm, decomposing the original problem into a plurality of sub-problems, and solving each sub-problem in a satellite respectively, wherein the algorithm convergence speed is effectively increased in a multi-user scene. The invention optimizes the user unloading decision aiming at the satellite edge computing network with limited resources, satellite movement and massive users so as to minimize network time delay and energy consumption.
Description
Technical Field
The invention relates to the technical field of mobile edges, in particular to a calculation unloading method considering satellite mobility in a satellite edge calculation network.
Background
Satellite networks have many incomparable advantages such as global coverage, flexible access, etc. Mobile edge computing (Mobile Edge Computing, MEC) refers to sinking computing resources located in the cloud center to the edge in order to reduce task processing latency and power consumption. The MEC is deployed on the satellite, forming a satellite edge computing network. The coverage of the satellite edge computing network is larger, the computing time delay is lower, and the satellite edge computing network formed by combining the satellite network and the edge computing is the development trend of the future network.
Compared with a ground base station, satellites are limited by power consumption, volume, weight and the like, and satellite resources are limited, so that the computing capacity of a single satellite is limited. The number of satellites in one constellation is numerous, and the total computing resource of the satellite network can be fully utilized to serve multiple users. Therefore, whether the user performs the computation offload and to which satellite is the key issue in the satellite edge computing network.
In a satellite edge computing network, on the one hand, satellites have high mobility, and the satellites are far away from users when performing task computation, resulting in interruption of the communication process. On the other hand, the coverage area of the satellite constellation is large, so that the number of users accessing the satellite is large. Therefore, when the calculation offloading is performed in the satellite edge calculation network, comprehensive consideration is required to provide effective offloading decisions for large-scale users under the condition of ensuring effective communication between the satellite and the users.
Disclosure of Invention
Aiming at the prior art, the invention provides a calculation unloading method considering satellite mobility in a satellite edge calculation network, optimizes user unloading decisions aiming at the satellite edge calculation network with limited resources, satellite movement and massive users, aims at minimizing network delay and energy consumption, and provides an ADMM algorithm to solve the optimization problem.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the calculation unloading method considering satellite mobility in the satellite edge calculation network comprises the following steps:
Step S1: taking a satellite edge computing network architecture with a high-orbit GEO satellite as a cloud, a low-orbit LEO satellite as an edge and a user as an end into consideration, and establishing a time delay and energy consumption model;
Step S2: aiming at the high-speed movement of the satellite, combining the satellite movement, the satellite coverage time and the calculation time, establishing a time delay model considering the satellite movement, and establishing an optimization problem of calculation unloading according to the time delay and the energy consumption model;
step S3: and decomposing the original problem into a plurality of sub-problems by using an alternating direction multiplication sub-method ADMM, and respectively solving each sub-problem on a satellite to obtain an optimal calculation unloading result.
Further, in step S1, the satellite edge computing network is defined to include a three-layer structure:
The GEO layer is composed of GEO satellites and is used as a cloud center; the LEO layer is composed of LEO satellites deployed with a mobile edge computing MEC server, the LEO satellites and the GEO satellites are communicated through interlayer links, and adjacent LEO satellites are communicated through inter-satellite links; the ground layer is composed of users with computing capability, the users only communicate with the LEO satellite, and the LEO satellite relays user tasks to the GEO satellite;
The user set is expressed as The LEO satellite and GEO satellite sets are represented asWherein m+1 represents GEO satellite; each user generates a computing task in a time slot; by usingRepresenting a userAn offloading decision corresponding to each satellite; Representing a user Whether or not the computational tasks of (a) are offloaded to LEO satellites，Representing a userWhether to offload tasks to GEO satellites; if it isAndAll zero, then the task will be calculated locally at the user.
Further, in step S1, the delay model of the user includes three parts, namely, delay of the user completing calculation locally, delay of the user completing calculation and unloading at the LEO satellite, and delay of the user completing calculation and unloading at the GEO satellite;
User' s Time delay for locally completing calculationThe method comprises the following steps:
wherein, Indicating the CPU cycles required for this task,Representing the local computing power of the user;
User' s At LEO satelliteTime delay for completing calculation and unloadingThe method comprises the following steps:
wherein, AndRespectively represent usersSatellite-to-ground transmission delay to access satellite a and satellite-to-ground propagation delay,AndRepresenting two adjacent LEO satellites respectivelyAndInter-satellite transmission delay of (2) and inter-satellite propagation delay,Indicating access to satellite a and satelliteIs used for the number of hops of (a),Representing a userMission of (C) to LEO satelliteCalculating time delay;
User' s Time delay for completing calculation and unloading at GEO satelliteThe method comprises the following steps:
wherein, AndRespectively represent the inter-layer propagation delay from the access satellite a to GEO satellite M +1,Representing a userIs calculated on GEO satellite m+1.
Further, in step S1, the energy consumption model of the user includes three parts, namely, the energy consumption of the user for completing the calculation locally, the energy consumption of the user for completing the calculation and the unloading at the LEO satellite, and the energy consumption of the user for completing the calculation and the unloading at the GEO satellite;
User' s Energy consumption to perform calculations locallyThe method comprises the following steps:
wherein, Is with the userA constant associated with the device CPU;
User' s At LEO satelliteEnergy consumption to complete computational offloadingThe method comprises the following steps:
wherein, AndRespectively represent usersSatellite-to-ground transmission energy consumption to access satellite a and two adjacent LEO satellitesAndIs used for the inter-satellite transmission energy consumption,Representing a userMission of (C) to LEO satelliteThe energy consumption is calculated;
User' s Energy consumption for completing calculation and unloading in GEO satelliteThe method comprises the following steps:
wherein, The interlayer transmission energy consumption from the access satellite a to the GEO satellite m+1 is represented.
Further, in step S2, for mobility of the LEO satellite, according to a relationship between the task calculation time and the satellite coverage time, time delays of the four scene analysis tasks in the calculation of the LEO satellite are divided to obtain a userMission of (C) to LEO satelliteCalculating the time delay of unloading;
Ignoring the energy consumption of the result returning process, wherein the energy consumption under four scenes has the same calculation expression, namely ；Representing LEO satellite m versus userCoverage time of (2); according to four scenarios, a time delay model of the satellite is established as follows:
(a) If it is At this time, the user finishes calculation and unloading in the satellite coverage time without considering the influence of satellite movement, and usesThe time delay representing the scene computation offload is computed as:
(b) If it is And the LEO satellite selected for unloading flies away from the user, at the moment, the user cannot finish the calculation unloading within the coverage time of the satellite, and the calculation result is returned to the user through the relay satellite for useThe time delay representing the scene computation offload is computed as:
wherein, Representing satellites during computationRelative to the userNumber of hops moved;
（c） And the LEO satellite selected for offloading flies to the user, over-ridding for a calculated time The time delay representing the scene computation offload is computed as:
（d） And the offloaded LEO satellite is selected to fly to the user, and overtake for the calculation time, The time delay representing the field computation offload is calculated as:
According to 、、AndA time delay model considering satellite movement is established and expressed by the following piecewise function:
By using AndRespectively representing the total time delay and the total energy consumption of the network; The calculation is as follows:
wherein, Representing a userThe time delay for computing the offload is done locally,Representing a userThe time delay for the computation of the offloading is done on the LEO satellite,Representing a userTime delay for completing calculation and unloading on GEO satellite;
The calculation is as follows:
wherein, Representing a userThe energy consumption of the computation offload is done locally,Representing a userAt LEO satelliteThe energy consumption of the unloading is calculated,Representing a userAnd (5) calculating the energy consumption of unloading at the GEO satellite.
Further, in step S2, according to the time delay, the energy consumption model and the time delay model considering satellite movement, the optimization problem of calculation offloading is expressed in the following form with satellite calculation resources as constraints:
Where obj is the offload cost, which is a weighted sum of latency and energy consumption, Is an index weight coefficient; (C1-C2) ensuring that each offload task can only be handled on a local or one satellite; (C3) Representing a computational resource constraint, wherein,Representing the CPU cycles required for a task,Representing satellitesIs the largest computational resource of (a).
Further, in step S3, a binary variable is addedConversion to continuous variable，; The converted problem form is as follows:
wherein, 。
Further, in step S3, for the optimization problem of computation offloading, a distributed optimization algorithm ADMM is used to solve, that is, the problem is split into a plurality of sub-problems, each of which is solved on a satellite, and the specific steps are as follows:
in the above-described problem, global variables Is inseparable; in order to make the problem separable so that each satellite solves the problem independently, a global variable is first introducedIs a local variable of (2); for the userUnloading satelliteIs provided withFor usersCorresponding satelliteA kind of electronic deviceA set of components, whereinIs thatIs used for the local variables of (a),Representing the userCorresponding satelliteIs the first of (2)Each sub-question at this time is of the form:
wherein, ; Consistent constraintForcing all local variables in the satellite to be consistent with the corresponding global variables; for each satellite, solving the sub-problems respectively;
for ease of description, the following set is defined as a viable set of local variables for the satellite:
then, the objective function of the local variable is given again:
According to the two formulas above, the equivalent description of the local problem is as follows:
In the above problems, there is a feasible set Is separable with respect to all satellites in the satellite edge computing network; moreover, when the local variable in each satellite is equal to the global variable corresponding to the satellite, the consensus of the problem can be maintained; the constraint guarantees consistency between all local and global variables and the problem is expressed in terms of an augmented lagrangian:
wherein, Representing the set of lagrangian multipliers,Is corresponding to each local variableIs a product of the lagrangian multipliers of (c),Is a penalty parameter for adjusting the convergence speed of the ADMM.
Further, in step S3, the solution is performed by using the ADMM, and the solution steps are as follows:
S3-1: setting the maximum iteration number as Iteration stop threshold，; And randomly select a set of initial offload decision vectors；
S3-2: judging the iteration timesWhether or not it is less than the maximum number of iterations; If the number is smaller than the preset number, executing the steps S3-3 and S3-4; otherwise, executing S3-6;
s3-3: each satellite Cyclically updating local unload variables according to the following formulaGlobal offload variablesLagrangian multiplier；
Wherein,Represent the firstThe lagrangian multiplier of the next iteration,AndRespectively represent the firstLocal and global variables at the time of the iteration,Is a penalty coefficient;
S3-4: updating iteration number ；
S3-5: judging whether the original residual error and the dual residual error are smaller than the following formulaAndIf the number is smaller than the preset number, executing S3-6; otherwise, returning to S3-3;
S3-6: outputting a continuous value ；
S3-7: for any userComparing satellitesCorresponding userA kind of electronic deviceSize, and will be maximumReducing to 1, and reducing the rest variables to 0; repeating the operation for all users until allAre all reduced to 0-1 variable；
S3-8: returning computation offload results。
The beneficial effects of the invention are as follows:
(1) Unloading the user task to the satellite for calculation, so that the user service request is responded quickly, and the resource and energy consumption is reduced;
(2) Analyzing four scenes of satellite movement, establishing a time delay model considering the satellite movement, and establishing an optimization problem of calculation and unloading according to the time delay and energy consumption model, so that the problem of high satellite movement speed is effectively solved;
(3) And solving the problem by using an ADMM algorithm, decomposing the original problem into a plurality of sub-problems, and solving each sub-problem in a satellite respectively, wherein the algorithm convergence speed is effectively increased in a multi-user scene.
Drawings
Fig. 1 is a schematic diagram of a satellite edge computing network according to an embodiment of the invention.
Fig. 2 is a schematic diagram of four switching scenarios of a satellite according to an embodiment of the present invention.
FIG. 3 is a flow chart of an embodiment of the present invention.
Fig. 4 is a flowchart of an ADMM-based computing offload algorithm according to an embodiment of the present invention.
FIG. 5 is a graph showing experimental results of an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the attached drawings.
Step S1: consider a satellite edge computing network architecture with high orbit (Geostationary earth Orbit, GEO) satellites as the cloud, low orbit (Low earthorbit, LEO) satellites as the edges, and users as the ends, and build a model of latency and energy consumption.
In step S1, a three-layer structure is defined in the satellite edge computing network, as shown in fig. 1:
(1) GEO layer: the GEO satellite has the advantages of large load, wide coverage and the like, and the relative position is fixed, so that the GEO satellite can be provided with a large amount of resources to serve as a cloud center.
(2) LEO layer: the LEO layer consists of LEO satellites deployed with mobile edge computation (Mobile Edge Computing, MEC) servers. LEO satellites communicate with GEO satellites via inter-layer links, and adjacent LEO satellites communicate via inter-satellite links. Because of the instability of the out-of-orbit links, the method only considers the mutual cooperation among the same-orbit satellites to carry out calculation unloading.
(3) Ground layer: the ground layer is composed of users with computing power. Because of the transmit power limitation, the user can only communicate with the LEO satellite, and the LEO satellite can relay the user tasks to the GEO satellite.
The user set is expressed as. LEO satellites and GEO satellite sets are represented as. Wherein M+1 represents a GEO satellite. Each user generates a computational task in a time slot. Use/>Representing user/>Corresponding to the offloading decision for each satellite. /(I)Representing user/>Whether or not to offload the computational tasks to LEO satellite/>，/>Representing a userWhether to offload tasks to GEO satellites. If/>And/>All zero, then the task will be calculated locally at the user.
According to the satellite edge computing network architecture shown in fig. 1, the time delay and energy consumption models of the users are respectively defined as follows:
The user's delay model includes three parts: the time delay calculated by the user at the local, the time delay calculated by the user at the LEO satellite and the time delay calculated by the user at the GEO satellite.
User' sDelay/>, of locally completing computationThe method comprises the following steps:
wherein, Representing the CPU cycles required for the task,/>Representing the local computing power of the user.
User' sAt LEO satellite/>Time delay/>, to complete computation offloadThe method comprises the following steps:
wherein, AndRespectively represent usersSatellite-to-ground transmission delay to access satellite a and satellite-to-ground propagation delay,AndRepresenting two adjacent LEO satellites respectivelyAndInter-satellite transmission delay of (2) and inter-satellite propagation delay,Indicating access to satellite a and satelliteIs used for the number of hops of (a),Representing a userMission of (C) to LEO satelliteAnd (3) calculating time delay.
User' sTime delay for completing calculation and unloading at GEO satelliteThe method comprises the following steps:
wherein, AndRespectively represent the inter-layer propagation delay from the access satellite a to GEO satellite M +1,Representing a userIs calculated on GEO satellite m+1.
The energy consumption model of the user comprises three parts: the energy consumption calculated by the user locally, the energy consumption calculated by the user at the LEO satellite and the energy consumption calculated by the user at the GEO satellite.
User' sEnergy consumption to perform calculations locallyThe method comprises the following steps:
wherein, Is with the userA constant associated with the device CPU.
User' sAt LEO satelliteEnergy consumption to complete computational offloadingThe method comprises the following steps:
wherein, AndRespectively represent usersSatellite-to-ground transmission energy consumption to access satellite a and two adjacent LEO satellitesAndIs used for the inter-satellite transmission energy consumption,Representing a userMission of (C) to LEO satelliteAnd (3) calculating energy consumption.
User' sEnergy consumption for completing calculation and unloading in GEO satelliteThe method comprises the following steps:
wherein, The interlayer transmission energy consumption from the access satellite a to the GEO satellite m+1 is represented. The GEO satellite has strong onboard capability and can supplement energy through solar energy, so the invention omits the calculation energy consumption of the GEO satellite.
Step S2: four scenes of satellite movement are analyzed aiming at the high-speed movement of the satellite, a time delay model considering the satellite movement is established, and the optimization problem of calculation unloading is established according to the time delay and energy consumption model;
In step S2, for mobility of the LEO satellite, according to a relationship between task calculation time and satellite coverage time, time delays of tasks during calculation of the LEO satellite are analyzed according to four scenes, and time delays of user tasks for completing calculation and unloading on the LEO satellite are obtained.
The invention ignores the energy consumption of the result returning process, so that the energy consumption under four scenes has the same calculation expression, such asAs shown. /(I)Representing LEO satellite m versus user/>Is used for covering the time of the cover. According to the four scenarios shown in fig. 2, a time delay model of the satellite is built as follows:
(a) If (3) At this time, the user can complete the calculation unloading within the satellite coverage time, so that the influence caused by the satellite movement is not considered, as shown in fig. 2 (a). Use/>The time delay representing the scene computation offload is computed as:
(b) If (3) And the LEO satellite selected to be unloaded flies away from the user, at the moment, the user cannot finish the calculation unloading within the coverage time of the satellite, and the calculation result is returned to the user through the relay satellite. As shown in FIG. 2 (b), byThe time delay representing the scene computation offload is computed as:
wherein, Representing satellite/>, during computationRelative user/>Number of hops moved.
(C) If (3)And the selected offloaded LEO satellite flies to the user, over-ridden for the calculation time, as shown in fig. 2 (c). Use/>The time delay representing the scene computation offload is computed as:
(d) If (3) And the offloaded LEO satellite is selected to fly to the user and over-ridden for the computation time, as shown in fig. 2 (d). Use/>The time delay representing the scene computation offload is computed as:
According to 、、AndA time delay model considering satellite movement is established and expressed by the following piecewise function:
By using And/>Representing the total delay and total energy consumption of the network, respectively. /(I)The calculation is as follows:
wherein, Representing user/>Time delay for locally completing computation offload,/>Representing user/>Time delay for completing calculation and unloading on LEO satellite,/>Representing user/>The time delay of the unloading is calculated on the GEO satellite.
Likewise, the number of the cells to be processed,The calculation is as follows:
wherein, Representing user/>Energy consumption/>, of locally performing computational offloadingRepresenting user/>At LEO satellite/>Energy consumption for completing computation offload,/>Representing user/>And (5) calculating the energy consumption of unloading at the GEO satellite.
According to the established time delay and energy consumption model and the established time delay model considering satellite movement, the invention uses satellite computing resources as constraint to express the optimization problem of computing and unloading as the following forms:
Where obj is the offload cost, which is a weighted sum of latency and energy consumption, Is an index weight coefficient. (C1-C2) ensuring that each offload task can only be handled on a local or one satellite; (C3) Representing computing resource constraints, wherein/>Representing the CPU cycles required for a task,/>Representing satellite/>Is the largest computational resource of (a).
Step S3: the original problem is decomposed into a plurality of sub-problems by using an alternate direction multiplication sub-method (ALTERNATING DIRECTION METHOD OF MULTIPLIERS, ADMM), and each sub-problem is solved on a satellite to accelerate the algorithm convergence speed.
The flow chart of the calculation unloading algorithm based on ADMM in the embodiment of the invention is shown in fig. 4, and the specific steps are as follows:
in step S3, a binary variable is added Conversion to continuous variable/>，/>. The converted problem form is as follows:
wherein, 。
For the problems, the invention adopts a distributed optimization algorithm ADMM to solve, namely the problem is split into a plurality of sub-problems, and each sub-problem is solved on a satellite respectively so as to accelerate the convergence speed of the algorithm. The specific steps are as follows:
in the above-described problem, global variables Is inseparable. In order to make the problem separable so that each satellite can solve the problem independently, a global variable/>, is first introducedIs a local variable of (a). For user/>Offloaded satellite/>Is provided withFor user/>Corresponding satellite/>/>A set of components, wherein/>For/>Local variable of/>Representing the user/>Corresponding satellite/>(1 /)Each sub-question at this time is of the form: /(I)
Wherein,. Consistent constraint/>All local variables in the satellite must be forced to agree with the corresponding global variables. The above sub-problem is solved separately for each satellite.
For ease of description, the following set is defined as a viable set of local variables for the satellite:
then, the objective function of the local variable is given again:
According to the two formulas above, the equivalent description of the local problem is as follows:
In the above problems, there is a feasible set Is separable with respect to all satellites in the satellite edge computing network. And, when the local variable in each satellite is equal to its corresponding global variable, a consensus of the problem can be maintained. The constraint guarantees consistency between all local and global variables and the problem is expressed in terms of an augmented lagrangian:
wherein, Representing the Lagrangian multiplier set,/>Is corresponding to each local variable/>Lagrangian multiplier,/>Is a penalty parameter for adjusting the convergence speed of the ADMM. The problem is solved by ADMM, and the solving steps are as follows:
S3-1, setting the maximum iteration number as Iteration stop threshold/>，/>; And randomly selects a set of initial offload decision vectors/>。
S3-2, judging the iteration timesWhether or not it is less than the maximum number of iterations/>; If the number is smaller than the preset number, executing the steps S3-3 and S3-4; otherwise, executing S3-6;
s3-3 each satellite Circularly updating local unload variables/>, according to the following formulaGlobal offload variablesLagrangian multiplier/>;
Wherein,Represents the/>Lagrangian multiplier for the next iteration,/>And/>Respectively represent the/>Local and global variables at iteration,/>Is a penalty coefficient.
S3-4: updating iteration number；
S3-5: judging whether the original residual error and the dual residual error are smaller than the following formulaAnd/>If the number is smaller than the preset number, executing S3-6; otherwise, returning to S3-3;
S3-6: outputting a continuous value ;
S3-7: for any userCompare satellite/>Corresponding user/>/>Size, and will be maximum/>Reducing to 1 and the remaining variables to 0. This operation is repeated for all users until all/>Are reduced to 0-1 variable/>。
S3-8: returning computation offload results。
Preliminary experiments were performed in order to demonstrate the effectiveness of the present invention. The method of the present invention was compared with Optimal, DRLCO, JTO-CCRO, random, and CL. In the CL, the task of the user is only calculated locally and is not selected to be unloaded; in Random, the user's task will offload Random selection to a local, LEO satellite or GEO satellite; in Optimal, solving by using a convex optimization tool box to obtain an Optimal unloading decision of each user; in JTO-CCRO, the minimum offload cost problem is decoupled into a computational offload sub-problem, satellite mobility is not considered, but resource allocation is considered, and potential gaming is used for solving. In DRLCO, the computational offloading process is expressed as a Markov decision process, employing an actor-critic network, to dynamically learn the optimal offloading decisions, without considering the mobility of the satellites. The comparison result is shown in fig. 5. It can be seen from the figure that the average cost of the network is lowest when using the proposed method. Thus, the method of the present invention is effective.
The above description is merely of preferred embodiments of the present invention, and the scope of the present invention is not limited to the above embodiments, but all equivalent modifications or variations according to the present disclosure will be within the scope of the claims.
Claims (5)
1. The calculation unloading method considering satellite mobility in the satellite edge calculation network is characterized in that: the method comprises the following steps:
Step S1: taking a satellite edge computing network architecture with a high-orbit GEO satellite as a cloud, a low-orbit LEO satellite as an edge and a user as an end into consideration, and establishing a time delay and energy consumption model;
In step S1, the satellite edge computing network is defined to include a three-layer structure:
The GEO layer is composed of GEO satellites and is used as a cloud center; the LEO layer is composed of LEO satellites deployed with a mobile edge computing MEC server, the LEO satellites and the GEO satellites are communicated through interlayer links, and adjacent LEO satellites are communicated through inter-satellite links; the ground layer is composed of users with computing capability, the users only communicate with the LEO satellite, and the LEO satellite relays user tasks to the GEO satellite;
The user set is represented as i= {1,2, i., I, the LEO satellite and GEO satellite sets are denoted as m= {1,2, m., M, m+1, wherein m+1 represents a GEO satellite; each user generates a computing task in a time slot; user i corresponds to the offloading decision for each satellite represented by a i＝{ai,1,ai,2,...,ai,M,ai,M+1; a i,m e {0,1} indicates whether user i's computing task is offloaded to LEO satellite m, a i,M+1 e {0,1} indicates whether user i's task is offloaded to GEO satellite; if both a i,m and a i,M+1 are zero, then the task will be calculated locally at the user;
In step S1, the delay model of the user includes three parts, namely, delay of the user completing calculation and unloading locally, delay of the user completing calculation and unloading at the LEO satellite, and delay of the user completing calculation and unloading at the GEO satellite;
time delay for user i to finish calculation locally The method comprises the following steps:
Where x i represents the CPU cycles required for the task, and f U represents the user's local computing power;
Time delay for user i to finish calculation and unloading at LEO satellite m The method comprises the following steps:
wherein, And/>Representing the satellite-to-ground transmission delay and satellite-to-ground propagation delay of user i to access satellite a,And/>Represents the inter-satellite transmission delay and the inter-satellite propagation delay of two adjacent LEO satellites m and m+1 respectively, and n A,m represents the hop count of the access satellite A and the satellite m,/>Representing the computation delay of user i's mission on LEO satellite m;
Time delay for user i to finish calculation and unloading in GEO satellite The method comprises the following steps:
wherein, And/>Respectively represent the interlayer transmission delay and interlayer propagation delay of the access satellite A to the GEO satellite M+1,/>Representing the computation delay of user i's mission on GEO satellite m+1;
step S2: aiming at the high-speed movement of the satellite, combining the satellite movement, the satellite coverage time and the calculation time, establishing a time delay model considering the satellite movement, and establishing an optimization problem of calculation unloading according to the time delay, the energy consumption model and the time delay model considering the satellite movement;
In step S2, aiming at mobility of the LEO satellite, according to a relation between task calculation time and satellite coverage time, time delays of tasks during calculation of the LEO satellite are analyzed according to four scenes, and time delays of tasks of a user i for completing calculation and unloading on the LEO satellite m are obtained;
Ignoring the energy consumption of the result returning process, wherein the energy consumption under four scenes has the same calculation expression, namely Representing the coverage time of LEO satellite m to user i; according to four scenarios, a time delay model of the satellite is established as follows:
(a) If it is At the moment, the user finishes calculation unloading within the satellite coverage time without considering the influence caused by satellite movement, and uses/>The time delay representing the scene computation offload is computed as:
(b) If it is And the LEO satellite selected to be unloaded flies away from the user, at the moment, the user cannot finish calculation unloading within the coverage time of the satellite, and the calculation result is returned to the user through the relay satellite and used/>The time delay representing the scene computation offload is computed as:
wherein, Representing the number of hops that satellite m moves relative to user i during the calculation;
(c) If it is And the LEO satellite selected for offloading flies to the user, is not overtop for the computation time, use/>The time delay representing the scene computation offload is computed as:
(d) If it is And the LEO satellite selected for offloading flies to the user and over-tops for a calculated time, forThe time delay representing the scene computation offload is computed as:
According to And/>A time delay model considering satellite movement is established and expressed by the following piecewise function: /(I)
The total time delay and the total energy consumption of the network are respectively represented by t total and e total; t total is calculated as:
wherein, Representing the delay of user i to finish computing offloading locally,/>Representing the time delay for user i to complete the computational offloading on LEO satellites,/>Representing the time delay of the user i for completing calculation and unloading on the GEO satellite;
e total is calculated as:
wherein, Representing the energy consumption of user i to locally complete the computation offload,/>Representing the energy consumption of user i to complete the computational offloading at LEO satellite m,/>The energy consumption of the user i for completing calculation and unloading at the GEO satellite is represented;
In step S2, according to the time delay, the energy consumption model and the time delay model considering satellite movement, the optimization problem of calculation unloading is expressed in the following form by taking satellite calculation resources as constraints:
obj:λttotal+(1-λ)etotal
Wherein obj is the unloading cost, the unloading cost is the weighted sum of time delay and energy consumption, and lambda is the index weight coefficient; C1-C2 ensures that each offloading task can only be processed on a local or one satellite; c3 represents a computational resource constraint, where x i represents the CPU cycles required for the task and Z m represents the maximum computational resource of satellite m;
step S3: and decomposing the original problem into a plurality of sub-problems by using an alternating direction multiplication sub-method ADMM, and respectively solving each sub-problem on a satellite to obtain an optimal calculation unloading result.
2. The method for computing offloading in a satellite-edge computing network considering satellite mobility of claim 1, wherein: in step S1, the energy consumption model of the user includes three parts, namely, the energy consumption of the user for completing the calculation locally, the energy consumption of the user for completing the calculation and the unloading at the LEO satellite, and the energy consumption of the user for completing the calculation and the unloading at the GEO satellite;
the energy consumption of user i to complete the calculation locally The method comprises the following steps:
Where ε i is a constant related to user i's device CPU;
energy consumption for user i to finish calculation and unloading in LEO satellite m The method comprises the following steps:
wherein, And/>Respectively representing the satellite-to-ground transmission energy consumption of a user i to an access satellite A and the inter-satellite transmission energy consumption of two adjacent LEO satellites m and m+1,/>Representing the computational power consumption of user i's mission on LEO satellite m;
Energy consumption for user i to finish calculation and unloading in GEO satellite The method comprises the following steps:
wherein, The interlayer transmission energy consumption from the access satellite a to the GEO satellite m+1 is represented.
3. The method for computing offloading in a satellite-edge computing network considering satellite mobility of claim 1, wherein: in step S3, binary variable a i,m is converted into continuous variable a' i,m,0≤a′i,m.ltoreq.1; the converted problem form is as follows:
min f(a′i,m)
wherein f (a' i,m)＝λttotal(a′i,m)+(1-λ)etotal(a′i,m).
4. A method of computing offloading in a satellite edge computing network taking into account satellite mobility as defined in claim 3, wherein: in step S3, for the optimization problem of computing offloading, a distributed optimization algorithm ADMM is used to solve, that is, the problem is split into a plurality of sub-problems, each of which is solved on a satellite, and the specific steps are as follows:
In the above problem, the global variable a' i,m is inseparable; in order to make the problem separable so that each satellite solves the problem independently, first, a local variable of the global variable a' i,m is introduced; for satellite m unloaded by user i, set K component sets for user i corresponding to satellite m, where/>For the local variable a' i,m, k ε M represents the kth component of user i for satellite M, where each sub-problem is of the form:
wherein, The consistency constraint C 4 forces all local variables in the satellite to be consistent with the corresponding global variables; for each satellite, solving the sub-problems respectively;
for ease of description, the following set is defined as a viable set of local variables for the satellite:
then, the objective function of the local variable is given again:
The equivalent description of the local problem is as follows:
In the above-described problem, the objective function with the feasible set Ω k is separable with respect to all satellites in the satellite edge computing network; moreover, when the local variable in each satellite is equal to the global variable corresponding to the satellite, the consensus of the problem can be maintained; the constraint guarantees consistency between all local and global variables and the problem is expressed in terms of an augmented lagrangian:
wherein, Representing the Lagrangian multiplier set,/>Is corresponding to each local variable/>P is a penalty parameter for adjusting the convergence speed of the ADMM.
5. The method for computing offloading considering satellite mobility in a satellite edge computing network of claim 4, wherein: in step S3, the solution is performed by ADMM, and the solution steps are as follows:
S3-1: setting the maximum iteration times as T and setting an iteration stop threshold epsilon 1＞0,ε2 to be more than 0; and randomly select a set of initial offload decision vectors
S3-2: judging whether the iteration times T are smaller than the maximum iteration times T or not; if the number is smaller than the preset number, executing the steps S3-3 and S3-4; otherwise, executing S3-6;
S3-3: each satellite m cyclically updates the local unloading variables according to the following formula And global unload variables/>Lagrangian multiplier/>
Wherein,Lagrangian multiplier representing the t-th iteration,/>And/>Respectively representing a local variable and a global variable in the t-th iteration, wherein ρ is a penalty coefficient;
S3-4: updating the iteration times t;
S3-5: judging whether the original residual error and the dual residual error are smaller than epsilon 1 and epsilon 2 according to the following formula, and executing S3-6 if the original residual error and the dual residual error are smaller than epsilon 1 and epsilon 2; otherwise, returning to S3-3;
S3-6: outputting a continuous value
S3-7: for any user i, comparing the satellite m with the corresponding user iSize, and will be maximum/>Reducing to 1, and reducing the rest variables to 0; this operation is repeated for all users until all/>All reduced to the 0-1 variable a i,m;
S3-8: and returning a calculation unloading result a i,m.
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